Fatehold Chronologist // Peer Review

Being prepared isn't a copiable value. If a permanent becomes a copy of a prepared creature, it won't be prepared. That permanent will have the alternative characteristics, though, and some other effect could cause it to become prepared later.

As an effect causes a creature with a prepare spell to become prepared (including effects that state that a creature "enters prepared"), that creature's controller creates a copy of that creature's prepare spell in exile. That copy remains in exile for as long as that permanent is on the battlefield and is prepared. That creature's controller may cast that copy as long as it remains in exile. As they cast it, that creature stops being prepared.

Only the current controller of a prepared creature can cast the copy of its prepare spell in exile. It doesn't matter who owns that creature or who controlled it when it became prepared.